There’s probably no good way to share the story of the Holocaust with a child. Who wants to taint an innocent with tales of the very worst of mankind, who wants to potentially terrify a soul whose most frightening image so far has probably been something like the Joker from “Batman”? How do you explain, to use the title of HBO’s new documentary, “The Number on Great-Grandpa’s Arm”?

This 20-minute film, premiering at 6 p.m. on Saturday, which is International Holocaust Remembrance Day, zeroes in on how one man, a Holocaust survivor, tells his 10-year-old great-grandson about the 20th-century nightmare. Gently, but never withholding truths, Jack Feldman, 90, talks to young Elliott about how he came by the blue tattoo, which he received at the Auschwitz concentration camp when he was 14. It’s a lovely, sweetly made little film, directed by Amy Schatz, that shows the bond between old man and young boy tightening the more they talk about it.

Just the respect and love in Elliott’s eyes as he looks up at Jack, and the warmth of their body language throughout the film, are worth the price of admission.

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Jack describes, in relatively plain language, how he was born in Poland, how his father made hats, and how, as Hitler gained power, Jews were rounded up, put in ghettos, and forced to sleep with 15 to 20 people in a single room. He describes being taken away, never to see his family again or to even find out what happened to them.

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Throughout, as Jack talks, his story is illustrated primarily with animation created by artist Jeff Scher for the film. Scher’s moving images, all painted in watercolor, have a childlike aura to them — the effect isn’t cartoonish in the least, but the ugliness and brutality are softened slightly for a child’s unblinking eye. It’s a smart approach, delivering reality through a mild filter of sorts.

We learn that, after the war, Jack got married and wound up in New York state, where he started a family and opened a fish store. And we hear, from one of his workers, that he is a good person, and that the experience didn’t destroy his compassion. “This is his number right here,” the guy says about Jack’s arm. “And he knows exactly what it means to be hungry. So if there’s anybody hungry, he’s gonna feed ’em, if you got money or not.”

As the narrator, Elliott is poised and affectionate. He is a wonderful stand-in for young viewers who might be ready to hear about the Holocaust. He listens carefully, aware that he is part of an increasingly essential exchange of information, particularly as survivors die out. “You need to know it to understand,” Elliott says, “to stop it from happening in future generations.”